Oversampled filter bank for subband processing

ABSTRACT

An oversampled filter bank structure that can be implemented using popular and efficient fast filter banks to allow subband processing of an input signal with substantially reduced aliasing between subbands. Even subbands (SB 0 , SB 2 , SB 4 , . . . ) of an input signal (x(n)) are frequency-shifted ( 212, 1012, 1012′, 1012″ ) prior to analysis filtering ( 214, 214′, 214″ ) at a 2× oversampled filter bank, subband processing ( 240, 240′, 240″ ), and synthesis filtering ( 216, 216′, 216″ ). A subsequent frequency-shift ( 218, 218′ ) returns the even subbands to their original band positions. The odd subbands (SB 1 , SB 3 , SB 5 , . . . ) are delayed ( 252 ) to compensate for the processing time of the frequency shifting. Separate analysis ( 214, 214 ′) and synthesis ( 216, 216 ′) filter banks may be provided for the even and odd subbands, or common complex analysis ( 284 ) and synthesis ( 286 ) filter banks may be used. In another embodiment, the subbands are processed in four subband paths (Paths  0, 1, 2, 3 ), and  4 × oversampling is used. A filter bank structure ( 1400 ) for 2-D data is also provided.

This application is a 35 U.S.C. 371 application of PCT/US99/28343, filedon Nov. 30, 1999.

BACKGROUND OF THE INVENTION

The present invention relates to a filter bank for use in digital signalprocessing, and in particular, to an efficient filter bank structurethat uses oversampling and separate odd and even subband processingpaths to reduce aliasing between subbands.

The digital filter bank is an enabling technology for modern audio andvideo processing systems, and, more recently, digital data communicationsystems such as Orthogonal Frequency-Division Multiplexing (OFDM). FIG.1 illustrates a typical conventional filter bank structure. A circuit100 processes an input digital signal x(n) in N separate paths. Ananalysis filter bank 120 includes respective analysis filters thatdecompose and transform the input signal x(n) into its frequency-domainsubband components xb(0), . . . ,xb(N−1) according to respectivetransfer functions H(0), H(1) . . . H(i), . . . H(N−1). The subbandcomponents can be processed by distinct subband processors SB(0), SB(1). . . SB(i), . . . , SB(N−1) of a subband processor 140 to betransformed into respective components yb(0), yb(1) . . . , yb(i), . . ., yb(N−1). Various types of subband processing can be performed.

A synthesis filter bank 160 reassembles and transforms the processedcomponents into an output signal y(n) using synthesis filters F(0),F(1), F(i), . . . F(N−1).

Many text books provide a good introduction to the theory of digitalfilter banks.

Of particular interest is the class of critically-sampled uniform filterbanks, which have found wide application in the areas of audio and videoprocessing. For example, the DCT (Discrete Cosine Transform) is used inthe MPEG-2 video compression engine, whereas TDAC (Time Domain AliasingCancellation) and Cosine-modulated filter banks have been standardizedinto the MPEG-2 audio compression algorithms and Dolby Lab's™ AC3compression algorithm.

While the efficiency of these filter banks makes them suitable for manysignal processing applications, they suffer from aliasing between thesubbands. Most practical filters have finite rejection at the Nyquistfrequency so the signals beyond the Nyquist frequency are notsufficiently attenuated prior to downsampling, and appear as aliasedcomponents in the downsampled signal. Most of these filter banks aredesigned to be “aliasing canceling”, which means that the synthesisfilter bank is specifically designed to account for, and cancel, thealiasing caused by the analysis filter banks. However, this cancellationproperty severely constrains the kind of processing that can beintroduced by the subband processors SB(0), . . . , SB(N−1). Forexample, a gain factor applied to one of the subband processors SB(i)will cause aliasing in the neighboring subbands, SB(i−1) and SB(i+1),during synthesis. This makes the use of such filter banks unsuitable forapplications such as subband equalizers or noise shaper.

To reduce aliasing, a higher order filter can be used. However, thisdecreases the temporal resolution of the filter banks as well as thecomputational efficiency since additional calculations are required.

Another approach is to try to avoid the aliasing in the first place, byoversampling the subband components of interest. However, aliasing isstill present between the subbands unless the oversampling ratioapproaches the number of subbands M. This approach also is notcomputationally efficient.

Accordingly, it would be desirable to provide a filter bank structurefor subband processing that avoids constraining the type of subbandprocessing, is computationally efficient, avoids aliasing betweensubbands, can be implemented using fast filter banks, and which has arelatively low filter order, and good temporal response and stop bandrejection.

The filter bank structure should be suitable for use with any type ofdigital input signal, including one-dimensional signals such as audiosignals, and two-dimensional signals such as video signals, and shouldallow any type of subband processing, including embedding of auxiliarydata, noise shaping, and equalizing.

The filter bank structure should allow the use of real or complex filterbanks.

The present invention provides a filter structure having the above andother advantages.

SUMMARY OF THE INVENTION

The present invention relates to an oversampled filter bank structurefor subband processing that can be implemented using popular fast filterbanks, such as FFT and cosine-modulated filter banks. Advantageously,aliasing between subbands is substantially reduced, thus allowingindependent processing of the subband signals. Also, the filter designcriteria is significantly relaxed, thus resulting in a lower prototypefilter order, better temporal response and higher stop band rejection.

In a particular embodiment, a digital filter apparatus processes andigital input signal to provide a corresponding output signal in whichsubband processing has been performed. A first frequency shifterfrequency-shifts a first plurality of subbands of the digital inputsignal (such as the even subbands SB0, SB2, . . . ) to providefrequency-shifted subbands. An oversampled analysis filter bank meansfilters the frequency-shifted subbands, along with a second plurality ofsubbands of the digital input signal (such as the odd subbands SB1, SB3,. . . ), according to an oversampling ratio that is selected to reducealiasing between adjacent ones of the frequency-shifted subbands, andbetween adjacent ones of the second plurality of subbands.

The oversampling ratio may be 2:1.

The oversampled analysis filter bank means may be implemented as a combfilter bank.

The first frequency shifter provides a _(π)/M radian frequency shift,where M is the total number of subbands output from the analysis filterbank means. Preferably, M_(≧)8.

The oversampled analysis filter means may be implemented as separatereal filters for processing the even and odd subbands separately inparallel paths, or as a single complex filter bank which processes theeven and odd subbands together. The filter banks may be M/2-band filterbanks.

In any case, a delay is provided for delaying the second plurality ofsubbands to compensate for a delay of the first frequency shifter.

The frequency shifter may be implemented using a critically-sampledcosine-modulated filter bank, or a Hilbert transformer, for example.

A subband processor may be provided for processing the frequency-shiftedsubbands and the second plurality of subbands after filtering thereof.The subband processing may involve any known technique, such asembedding of auxiliary data, noise shaping and so forth.

After subband processing, an oversampled synthesis filter means isprovided for filtering the frequency-shifted subbands (e.g., evensubbands) and the second plurality of subbands (e.g., odd subbands)after processing thereof at the subband processor.

A second frequency shifter shifts the already frequency-shifted subbandsafter filtering thereof at the synthesis filter means in a shiftdirection opposite to a shift direction of the first frequency shifter.Moreover, a second delay delays the second plurality of subbands tocompensate for a delay of the second frequency shifter.

Subsequently, a combiner combines all subbands to provide a digitaloutput signal corresponding to the digital input signal.

Analogous to the analysis filter bank means, the synthesis filter bankmeans may include separate real oversampled synthesis filter banks forthe even and odd subbands, or a single complex synthesis filter bank.

Importantly, when the frequency shifters use cosine-modulated analysisand synthesis filter banks, proper frequency axis reversal is applied toeach subband to maintain the orientation of the subband data.

Also, in the frequency shifter, to avoid discarding data from thehighest even subband at the analysis filter of the frequency shifter, afrequency rotation scheme can be used where this data is fed to thelowest subband of the synthesis filter of the frequency shifter.

In an optional embodiment, a digital filter apparatus provides 4×oversampling to further reduce the likelihood of aliasing. An inputsignal is processed in four parallel paths, three of which includefrequency shifters for providing shifts of _(π)/M, _(π)/2M, and −_(π)/2Mradians, and one of which includes a delay for compensating for aprocessing time of the frequency-shifters.

The four sets of subbands are processed at an oversampled analysisfilter bank means with an oversampling ratio (e.g., 4:1) that isselected to reduce aliasing between adjacent subbands in each set.

In a further optional embodiment, filtering of two-dimensional data isprovided.

Corresponding methods are also presented.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a typical conventional filter bank structure.

FIG. 2( a) illustrates a generalized filter structure with2×-oversampled filter banks in odd and even subband paths in accordancewith the present invention.

FIG. 2( b) illustrates a filter structure with 2×-oversampled realfilter banks in odd and even subband paths in accordance with thepresent invention.

FIG. 2( c) illustrates a filter structure with a 2×-oversampled complexfilter bank in accordance with the present invention.

FIG. 3( a) illustrates the spectrum for even subbands in accordance withthe present invention.

FIG. 3( b) illustrates the spectrum for odd subbands in accordance withthe present invention.

FIG. 4( a) illustrates a critically-sampled cosine-modulated frequencyupshifter in accordance with the present invention.

FIG. 4( b) illustrates frequency axis reversal for a frequency shifterin accordance with the present invention.

FIG. 5 illustrates a Hilbert Transform frequency shifter in accordancewith the present invention.

FIG. 6 illustrates a critically-sampled cosine-modulated frequencydownshifter in accordance with the present invention.

FIG. 7 illustrates a prototype filter design for analysis and synthesisfilter banks in accordance with the present invention.

FIG. 8 illustrates a comb filter bank structure in accordance with thepresent invention.

FIG. 9 illustrates a graphical realization of one-dimensional filterbank processing in accordance with the present invention.

FIG. 10 illustrates a filter structure for one-dimensional filter bankprocessing with 4×-oversampled filter banks in four subband paths inaccordance with the present invention.

FIG. 11( a) illustrates the subband structure for Path 0 of the filterof FIG. 10 in accordance with the present invention.

FIG. 11( b) illustrates the subband structure for Path 1 of the filterof FIG. 10 in accordance with the present invention.

FIG. 11( c) illustrates the subband structure for Path 2 of the filterof FIG. 10 in accordance with the present invention.

FIG. 11( d) illustrates the subband structure for Path 3 of the filterof FIG. 10 in accordance with the present invention.

FIG. 12( a) illustrates an original 2-D signal (image) region withseveral subregions for processing in accordance with the presentinvention.

FIG. 12( b) provides a graphical depiction of a conventional 2-D,critically-sampled filter bank.

FIG. 13( a) provides a graphical depiction of a path with no frequencyshift (Path 0) in a 2-D, over-sampled filter bank in accordance with thepresent invention.

FIG. 13( b) provides a graphical depiction of a path with a horizontalfrequency shift (Path 1) in a 2-D, over-sampled filter bank inaccordance with the present invention.

FIG. 13( c) provides a graphical depiction of a path with a verticalfrequency shift (Path 2) in a 2-D, over-sampled filter bank inaccordance with the present invention.

FIG. 13( d) provides a graphical depiction of a path with horizontal andvertical frequency shifts (Path 3) in a 2-D, over-sampled filter bank inaccordance with the present invention.

FIG. 13( e) provides a graphical depiction of the frequency regions thatare processed in FIGS. 13( a)–13(d) in a 2-D, over-sampled filter bankin accordance with the present invention.

FIG. 14 illustrates a real filter structure for two-dimensional filterbank processing with 2×-oversampled real filter banks in four subbandpaths in accordance with the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to a filter bank for use in digital signalprocessing to prepare a signal for subband processing.

FIG. 2( a) illustrates a generalized filter structure with2×-oversampled filter banks in odd and even subband paths in accordancewith the present invention.

The filter apparatus 165 processes the input signal x(n) in an evensubband path 170 and an odd subband path 180. The even path 170 includesan M/2-band even subband oversampled analysis filter bank 172, and anM/2-band even subband oversampled synthesis filter bank 174. Similarly,the odd path 180 includes an M/2-band odd subband oversampled analysisfilter bank 182, and an M/2-band odd subband oversampled synthesisfilter bank 184.

A subband processor can be provided between the filters 172 and 174, andbetween the filters 182 and 184.

A combiner 175 receives the output of the filter 174, x_(even), and theoutput of the filter 184, x_(odd), to provide the output signal y(n).

FIG. 2( b) illustrates a filter structure with 2×-oversampled realfilter banks in odd and even subband paths in accordance with thepresent invention.

Here, a more specific implementation of the generalized structure ofFIG. 2( a) is provided.

The filter apparatus 200 processes the input signal x(n) in an evensubband path 210 and an odd subband path 250. The even path 210 includesa _(π)/M frequency shifter 212 and an M/2-band oversampled analysisfilter bank 214. The odd path 250 includes a delay 252, whichcompensates for the processing time of the frequency shifter 212, and anM/2-band oversampled analysis filter bank 214′, which is the complementof the filter bank 214.

A subband processor 240 receives the respective even and odd subbanddata, s_(even) and s_(odd), respectively, of the input signal x(n) fromthe filters 214 and 214′, respectively. The subband processing caninclude providing auxiliary data in each subband, harmonicanalysis/synthesis as used in pitch-preserving timecompression/expansion of audio, audio compression, and OFDM andtransmultiplexers (transcoding multiplexers) as used in digitalcommunications. For example, advantageous subband processing techniquesare disclosed in commonly-assigned U.S. Pat. Nos. 5,822,360 and5,937,000. The E-DNA® data processing system of Solana TechnologyDevelopment Corporation, San Diego, Calif., USA, is an example of suchtechnology.

The even and odd subbands may be processed using separate and/or commoncircuitry at the subband processor 240.

The data output from the subband processor 240 in the even path 210,s_(even)′, is provided to an M/2-band synthesis filter bank 216 that isproperly matched to the analysis filter bank 214, and a −_(π)/Mfrequency shifter 218. The data output from the subband processor 240 inthe odd path 250, s_(odd)′ is provided to an M/2-band synthesis filterbank 216′ that is properly matched to the analysis filter bank 214′, anda delay 258, which compensates for the processing time of the frequencyshifter 218.

A combiner 260 receives x_(even) and x_(odd) to provide the final outputsignal y(n).

Note that the frequency shifting is provided in the even subband path toallow the use of fast filter banks. Without this frequency shifting, thedownsampling edges would land on the center of the passband of interest.

Additionally, while the frequency shifter 212 is shown as an upshifterand the frequency shifter 218 is shown as a downshifter, the oppositemay be used.

M/2 is the downsampling ratio at the filters 214 and 214′, and theupsampling ratio at the filters 216 and 216′. M is the total number ofsubbands output from the analysis filter banks 214 and 214′ togetherwhen 2× oversampling is used.

M=32 (M/2=16) has been used satisfactorily by the present inventors. Mshould preferably be selected as a multiple of two to allow the use ofefficient algorithms, such as the DFT and FFT, in the filterimplementation. For practical purposes, M=8 as a minimum. The efficiencyof the fast filter banks does not become substantial unless M>>log₂(M).

FIG. 2( c) illustrates a filter structure with a 2×-oversampled complexfilter bank in accordance with the present invention.

Like-numbered elements correspond to one another in the figures.Additionally, the prime symbol (ex: 200′) denotes related elements.

Here, a single complex M/2-band analysis filter bank 284 is used insteadof having separate filter banks for the odd and even subbands. Acombiner 245 combines the even subband data x′ with the delayed, oddsubband data x_(d) to form the complex value x′+jx_(d).

After subband processing at the processor 240′, a correspondingsynthesis filter 286 is used to recover the even subband data x_(even)′and odd subband data x_(odd)′.

In FIGS. 2( b) and 2(c), note that x_(even)′ and x_(odd)′ are full-banddata signals, whereas s_(even)′ and s_(odd)′ are subband data signals.

The subband processing is the same in both processors 240′ and 240.

FIG. 3( a) illustrates the subband spectrum for even subbands inaccordance with the present invention.

A horizontal axis 310′ denotes frequency, _(ω), while a vertical axis320′ denotes the magnitude of the spectrum X_(even)(_(ω)) of the evensubband values just prior to recombining with the odd subband values toform the output signal y(n).

The end-to-end filter response or transfer function isX_(even)(_(ω))/X(_(ω)) using the notation of FIGS. 2( a)–2(c).

SB0, SB2 and SB4 denote the zeroeth, second and fourth subbandsrespectively. SB0 extends between 0 and _(π)/M, while its complexconjugate, SB0*, extends from −_(π)/M to 0. SB2 extends between _(π)/Mand 3_(π)/M, and SB3 extends between 3_(π)/M and 5_(π)/M. SB2* extendsbetween −_(π)/M and −3_(π)/M, although part of it is not shown.

The actual passbands of the even subbands are shown at 337, 338, 340 and342, while the corresponding idealized passbands, having a width of_(π)/M, are shown at 337′, 338′, 340′ and 342′, respectively.

FIG. 3( b) illustrates the subband spectrum for odd subbands inaccordance with the present invention.

A horizontal axis 310 denotes frequency, _(ω), while a vertical axis 320denotes the magnitude of the spectrum X_(odd)(_(ω)) of the odd subbandvalues just prior to recombining with the even subband values to formthe output signal y(n). The end-to-end response or transfer function isX_(odd)(_(ω))/X(_(ω)) using the notation of FIGS. 2( a)–(c).

SB1, SB3 and SB5 denote the first, third and fifth subbands,respectively. For example, SB1 extends between 0 and 2_(π)/M, SB3extends between 2_(π)/M and 4_(π)/M, and SB5 extends between 4_(π)/M and6_(π)/M. SB1* denotes the complex conjugate of SB1, and extends between0 and −2_(π)/M. Not all subbands are shown. For example, with M/2=16,subbands SB1, SB3, SB5, SB7, SB9, SB11, SB13 and SB15 are present in theodd subband path.

The actual passbands of the odd subbands are shown at 330, 332, 334 and336, while the corresponding idealized passbands, having a width of_(π)/M and a sharp cut-off response, are shown at 330′, 332′, 334′, and336′, respectively.

Referring to FIGS. 3( a) and 3(b), there are two important points tonote. First, unlike the critically-sampled counterpart, the pass bands330, 332, 334, 336, 338, 340, 342, . . . of the oversampled subbandsSB1*, SB1, SB3, SB5, SB0, SB2 and SB4, . . . , respectively, occupy lessthan the available bandwidth, 2_(π)/M. In contrast, a critically-sampledsignal utilizes the entire subband bandwidth.

With the present invention, each subband has very little signal energyaround its band edges 331, 333, 335, 350, 352, 354 . . . Therefore,little or negligible aliasing between subbands is introduced by thefilter banks 214, 214′ and 284. The oversampling ratio is determined bythe ratio of the available bandwidth to the utilized passband, and isusually chosen to be two to minimize computation and implementationcomplexity, although other ratios can be used.

Second, each of the subband paths 210, 250 has only M/2 subbands, butwhen we combine the two paths, there are a total of M subbands (outputfrom the filter bank 284), which cover the full bandwidth of the signalspace, and thus the filters 200 or 200′ overall each comprise an M-bandoversampled filter bank.

Referring again to FIG. 2( b), in the one-dimensional (1-D) filter 200,the analysis filter banks 214, 214′ are complements of one other, as arethe synthesis filter banks 216, 216′. For the 1-D oversampled filterbanks, the following design considerations should be taken into account.Namely, the difference in band alignment in the even and odd subbandpaths implies that two different filter banks need to be realized.Moreover, the even subband path is not easily realizable conventionally,since the subband centers are at multiples of _(π)/M, which is where thedownsampling/aliasing occurs with most fast filter banks algorithm.

However, the 2× oversampled filter banks of FIGS. 2( b) and 2(c) solvethe aforementioned problems. In particular, the M/2 samples of x(n) arereplicated in two paths, with one path (even path 210) going to thefrequency shifter 212 of _(π)/M radians, and the other path (odd path250) going through the delay line 252, which compensates for the delayintroduced by the frequency shifter 212.

Two sets of identical oversampled M/2-band analysis filter banks 214,214′ are used for decomposing the even and odd sequences. For M/2 timedomain samples, this results in 2*M/2=M subband samples total.

After the subband processing at the subband processor 240, the subbandssamples are reassembled/synthesized into the odd and even time-domainsequences with M/2 samples using two sets of identical oversampledM/2-band synthesis filter banks 216, 216′.

The synthesized even sequence is frequency shifted back by −_(π)/Mradians at the shifter 218. The synthesized odd sequence is delayed atthe delay 258 to align with the even path 210.

The odd and even sequences are added together at the combiner 260 toform M/2 time domain samples, y(n). Note that x(n) consists of asequence of M/2 samples, for which there will be a corresponding M/2samples of y(n), which is the reconstructed version of x(n).Oversampling occurs since M/2 samples of x(n) are transformed into Msamples of s_(even) and s_(odd) combined in the subband domain. Thus,the transformation is considered to be over-complete since it uses moresamples than is fundamentally necessary to represent the originalsequence.

The frequency shifters 212, 218 can be realized in a variety of ways, asdiscussed below.

FIG. 4( a) illustrates a critically-sampled cosine-modulated frequencyupshifter in accordance with the present invention.

The frequency upshifter 212′ receives the input signal x(n), having thespectral representation X(_(ω)), and outputs the signal x′(n), havingthe spectral representation X′(_(ω))=X(_(ω)−_(π)/M).

This approach to frequency shifting uses an M-band (or multiple thereof)cosine-modulated filter bank to perform the frequency shifting. At ananalysis filter portion 405 of the frequency shifter 212′, a time-domaintransfer function h(n) 410 decomposes the time sequence x(n) into Msubband samples, e.g., in paths 420, 430, 440, . . . , 450. For example,SB0 data is provided in path 420, SB2 data is provided in path 430, andso forth.

In each path, the subband samples are downsampled by a factor of M at acorresponding downsampler 422, 432, 442, . . . , 452, andcosine-modulated at a corresponding modulator 424, 434, 444, . . . 454.

The samples from the last (Mth) subband (cosine modulation index M−1) inpath 450 are discarded. This is acceptable for many applications, suchas wide-band audio applications, because the last subband usuallycontains noise with little signal energy. For example, if an audiosignal having a spectrum from 0 to 24 KHz is represented by M=32subbands, the last band that is discarded has components near 24 KHz,which do not carry significant information for the human listener.Moreover, the discarded subband provides a guard band that can avoidchannel interference.

However, if desired, a frequency rotation scheme can be employed wherethe highest subband output from the analysis filter 405, in path 450 isfed to the modulator 426 of the lowest subband of the synthesis filter406, in path 420. All information in x(n) can therefore be retained.

The subband samples in each path are fed to the next higher subband atthe synthesis filter 406 of the frequency shifter 212′, and the zeroethsubband is set to zero at modulator 426. Frequency axis reversalfunctions 461–463 are used due to the structure of the cosine-modulatedfilter banks, as discussed further in connection with FIG. 4( b).Frequency axis reversal for a band-limited sequence can be expressed as:x′(n)=x(n)*exp(j* _(π) *n)

In an actual implementation, this is equivalent to: x′(n)=x(n)*(−1)^(n),which flips the sign (polarity) of every other sample. This function canbe incorporated into the synthesis filter bank 406, but is shown asbeing separate in FIG. 4( a) for clarity.

The samples of SB0, in path 420, are provided to modulator 436, in path430. The samples of SB2, in path 430, are provided to modulator 446, inpath 440, and so forth. Generally, the samples in each subband in theanalysis filter bank 405 are fed to the next higher subband in thesynthesis filter bank 406.

Cosine modulators 426, 436, 446, . . . , 448 demodulate the subbandsamples from the next lower subband of the analysis filter 405 andprovide them to respective upsamplers 428, 438, 448, . . . 458, forupsampling by a factor of M. The resulting data is provided to afunction f(n) 460, which re-assembles the samples in proper sequence toobtain the time sequence x′(n), which is shifted by _(π)/M radiansrelative to x(n). This method is fairly efficient, but the delay islimited by the delay of the M-band filter banks.

A second approach for frequency shifting uses an M-band (or multiplethereof, e.g., 2M, 3M, . . . ) Discrete Fourier Transform (DFT) type offilter bank such as used in Time Domain Aliasing Cancellation (TDAC).See J. P. Princen et al., Analysis/Synthesis filter bank design based ontime domain aliasing cancellation, ASSP-34, October 1986. The structureis similar to the first approach. Specifically, this approach isslightly slower than the cosine-modulated filter bank, but has theadvantage that we can choose the number of subbands without worryingabout frequency reversal, discussed above.

With the second approach, we assume a N*M band TDAC filter bank, where Nis an integer. To realize a frequency shift of _(π)/M,analysis/synthesis filters are provided back-to-back with the followingrelationships:

-   -   sa(0)-->ss(N)    -   sa(1)-->ss(N+1)    -   sa(2)-->ss(N+2)        -   :    -   sa(i)-->ss(N+i),        where sa(i) is the analysis subband output at index i, and ss(i)        is the synthesis subband input at index i.

FIG. 4( b) illustrates frequency axis reversal for a frequency shifterin accordance with the present invention. Frequency axis reversal is aninherent characteristic of cosine-modulated filter banks.

The spectrum of X(_(ω)) is shown at 470. After processing at theanalysis filter 405 of the frequency shifter 212′, each (non-discarded)subband undergoes frequency axis reversal, as shown at 475. To correctthis, a corresponding reversal must be implemented, as shown at 480. Thecorrected subbands can then be input to the synthesis filter 406 of thefrequency shifter 212′ to provide the frequency-shifted subbandsX(_(ω)−_(π)/M) as shown at 480.

Essentially, a first set of every other subband output from the analysisfilter bank 405 contains signals that are frequency axis flipped, i.e.,0_(→π) and _(π→)0. A second set of the remaining alternate subbands willbe frequency axis flipped after processing at the synthesis filter 406.However, by routing the subband data into the next higher subband forfrequency upshifting, we are feeding non-flipped signals into thesynthesis filter bank, which would attempt to flip these subbandsignals. Proper frequency axis reversal for each subband avoids thisproblem.

An analogous result is achieved for frequency downshifting, as discussedin connection with FIG. 6, with frequency axis reversal functions661–663.

FIG. 5 illustrates a Hilbert Transform frequency shifter in accordancewith the present invention.

A third approach for implementing the frequency shifters 212 or 218 ofFIGS. 2( b) and 2(c) uses a Hilbert transformer with a complexmodulator. Specifically, the frequency shifter 212″ includes a HilbertTransformer 510, a complex modulator 520, and a function 530 for obtainthe real portion of the output of the modulator 520.

An ideal Hilbert transformer is an all-pass filter than imparts a 90°phase shift on the input signal.

The frequency response is specified as:H(_(ω))=−j for 0<ω≦π=j for −π<ω<0.

The Hilbert transformer can be implemented using a Fast FourierTransform (FFT) or a Finite Impulse Response (FIR) filter, for example.The Hilbert transform of the sequence is then modulated with a complexmodulator 520 with center frequency at _(π)/M, to achieve a frequencyupshift. The real part of the modulated sequence represents thefrequency-shifted version of the original time-domain sequence.

The frequency shifter 212″ can be used to achieve a frequency downshiftby using exp(−j_(π)/M) instead of exp(j_(π)/M) at the modulator 520. Theinput signal to the frequency shifter is then x_(even)′ (n), and theoutput signal is x_(even)(n).

FIG. 6 illustrates a critically-sampled cosine-modulated frequencydownshifter in accordance with the present invention.

The frequency downshifter 218′ receives the input signal x_(even)′ (n),having the spectral representation X_(even)′ (_(ω)), and outputs thesignal x_(even)(n), having the spectral representationX_(even)(_(ω))=X_(even)′ (_(ω)+_(π)/M).

The frequency downshifter 218′, which includes subband paths 620, 630,640, . . . , 650, is analogous to the frequency upshifter 212′. Ananalysis filter bank 605 and synthesis filter bank 606 correspond to theanalysis filter bank 405 and synthesis filter bank 406, respectively, ofFIG. 4( a), except each modulator 426, 436, 446, . . . , 448 receivessubband samples from the next higher (instead of lower) subband from theanalysis filter bank 605.

Frequency axis reversal functions 661–663 are also provided. They areanalogous to the reversal functions 461–463, as discussed in connectionwith FIGS. 4( a) and 4(b).

FIG. 7 illustrates a prototype filter design for analysis and synthesisfilter banks in accordance with the present invention.

In accordance with a critical aspect of the present invention, theoversampled M/2-band filter banks 214, 214′, 216 and 216′, along withthe complex filters 284 and 286, may be implemented as comb filters. Acomb filter may be viewed as a filter in which nulls occur periodicallyacross the frequency band. The comb filter structure of the presentinvention is realized using a modified form of cosine-modulated filterbank, which can be implemented with fast transforms such as the DCT orFFT. Other uniform filter banks may be used, such as a pseudo-QuadratureMirror Filter (QMF), as described in J. H. Rothweiler, PolyphaseQuadrature Filters—A New Subband Coding Technique, InternationalConference on Acoustics, Speech and Signal Processing (ICASSP), 1983.TDAC can also be used with appropriate modification.

Consider an M/2-band cosine-modulated filter bank. In a conventional,critically-sampled implementation, the prototype filter is designed tohave a bandwidth of _(π). In the present invention, the prototype filteris designed to have a bandwidth of _(π)/2. The response 730 of thecorresponding comb filter is shown in FIG. 7. A horizontal axis 710indicates frequency, while a vertical axis 720 indicates the magnitudeof the response, in decibels (dB). After the cosine modulation, a seriesof non-overlapping band-pass filters result which have band edges atmultiples of _(π)/4 and 3_(π)/4, respectively. The effective bandwidthof the pass band 750 is therefore _(π)/2. Note that an attenuation of−40 dB can be considered to represent an amplitude of essentially zero.

The stop band rejection of the filter is designed to be low enough sothat aliasing is small or negligible at 0 and _(π). Stop bands 740 and760 are provided between 0 and _(π)/4, and between 3_(π)/4 and _(π),respectively.

An additional benefit when designing this prototype filter is that weare no longer constrained by the severe aliasing cancellation matrix,discussed in P. P. Vaidyanathan, Multirate System And Filter Banks.Prentice Hall 1993, as with the critically-sampled case, thus yieldingadditional freedom in the design. Effectively, the filter order can bereduced substantially to provide better temporal resolution, and toachieve improved stop band rejection characteristics.

Note that the response 730 applies to both the analysis and synthesisfilter banks since, in the design of a cosine-modulated filter bank, oneonly needs to specify the prototype filter characteristics, and theresponse of the analysis and synthesis filters will be dictated by theprototype filter.

FIG. 8 illustrates a comb filter bank structure in accordance with thepresent invention.

The circuit 800 can perform the functions of the filter 214, subbandprocessor 240, and filter 216 of FIG. 2( b), or the filter 214′, subbandprocessor 240, and filter 216′ of FIG. 2( b).

An analysis comb filter bank 214″ includes a transfer function h(n) 810for providing the input signal in M/2 subbands, downsamplers 820, 822, .. . , 824, 826 for each of the M/2 even or odd subbands, andcorresponding cosine modulators 830, 832, . . . , 834, 836. Afterprocessing at the subband processor 240′, the even or odd subband datais processed at a synthesis comb filter bank 216″, which includes cosinemodulators 840, 842, . . . , 844, 846, corresponding M/2 upsamplers 850,852, . . . , 854, 856, and a transfer function f(n) 860 that assemblesthe subband data to provide the output x_(even)′ (n) or x_(odd)′ (n).

FIG. 9 illustrates a graphical realization of one-dimensional filterbank processing in accordance with the present invention.

The graphical illustration shows how the oversampled filter banks arerealized with the frequency shifter and comb filter banks alreadydiscussed.

For simplicity, only a portion of the actual spectrum X(_(ω)) (915) ofthe input signal x(n), i.e., from 0 to 5_(π)/M is shown. A number ofsubband portions A-J are shown.

For the processing of the odd subbands, X_(d)(_(ω)) (920) is formed bydelaying X(_(ω)). The passbands of the oversampled filter banks areshown at 922. The resulting odd subband samples S_(odd)(_(ω)) (924),which includes subband portions B, C, F, G and J, occupy only one-halfof the available subband width, 2_(π)/M. After a delay, X_(odd)(_(ω))(926) is formed, whose spectrum is essentially the same as S_(odd)(_(ω))(924).

For the processing of the even subbands, X′(_(ω)) (930) is formed byfrequency-shifting X(_(ω)) by _(π)/M. The passbands of the oversampledfilter banks are shown at 932. The resulting even subband samplesS_(even)(_(ω)) (934), including subband portions A, D, E and H, occupyonly one-half of the available subband width, 2_(π)/M. After a −_(π)/Mfrequency downshift, X_(even)(_(ω)) (936) is formed.

The subband values X_(odd)(_(ω)) and X_(even)(_(ω)) are then combined toform the full-band digital output signal Y(_(ω)) (950).

FIG. 10 illustrates a 2M-band filter (e.g., four, M/2-band filters) with4×-oversampled filter banks with four subband paths in accordance withthe present invention.

The filter structure 1000 includes four subband processing paths, i.e.,Path 0 (1010), Path 1 (1020), Path 2 (1030), and Path 3 (1040). Path 0(1010) includes a _(π)/M frequency shifter 1012, an M/2-band analysisfilter bank 1014, an M/2-band synthesis filter 1016, and a −_(π)/Mfrequency shifter 1018. Each synthesis filter bank receivescorresponding data from the subband processor 240″. Path 1 (1020)includes a _(π)/2M frequency shifter 1012′, an M/2-band analysis filterbank 1014′, an M/2-band synthesis filter 1016′, and a −_(π)/2M frequencyshifter 1018′.

Note that the frequency shift functions described herein can beimplemented as discussed previously (e.g., in connection with FIGS. 4(a), 4(b), 5 and 6) with modification as required for the magnitude anddirection of frequency shift.

Path 2 (1030) includes a delay 252, an M/2-band analysis filter bank1014″, an M/2-band synthesis filter 1016″, and a delay 252′. The delay252 compensates for the processing time of the frequency shifters 1012,1012′, and 1012″, while the delay 252′ compensates for the processingtime of the frequency shifters 1018, 1018′, and 1018″.

Path 3 (1040) includes a −_(π)/2M frequency shifter 1012″, an M/2-bandanalysis filter bank 1014″, an M/2-band synthesis filter 1016″, and a_(π)/2M frequency shifter 1018″.

With this scheme, each successive subband is processed in a successiveone of the Paths 1010, 1020, 1030, or 1040. For example, assuming 32subbands are used, i.e., numbered SB0-SB31, SB0, SB4, SB8, . . . areprocessed in Path 0 (1010), SB1, SB5, SB9, . . . are processed in Path 1(1020), SB2, SB6, SB10, . . . are processed in Path 2 (1030), and SB3,SB7, SB11, . . . are processed in Path 3 (1040).

The filter 1000 could optionally be modified to use one or two complexfilters, instead of four real filters, based on the discussion of FIG.2( c).

FIG. 11( a) illustrates the subband structure for Path 0 of the filterbank of FIG. 10 in accordance with the present invention.

The pass bands 1112, 1116, 1120, . . . of the 4× oversampled subbandsSB0*, SB0, SB4, SB8, . . . occupy only about one-fourth of the availablebandwidth, 2_(π)/M. The corresponding idealized pass bands are shown at1112′, 1116′, 1120′, . . . , respectively. Specifically, only about_(π)/2M radians is occupied by each subband, which leaves a substantialregion with little signal energy around the band edges 1110, 1114, 1118,. . . Therefore, little or negligible aliasing between subbands isintroduced by the filter structure 1000.

X_(Path-0)(_(ω)) designates the signal in Path 0 (1010), as shown inFIG. 10.

A similar result is achieved for the other subbands, as discussed below.

Generally, a primary benefit of 4× oversampling that there is even lessof a chance of aliasing than with 2× oversampling. The present inventorhas found that −40 dB attenuation at the band edges is more than enoughfor most practical purposes. However, there may be cases where theapplication demands even more attenuation. One way to achieve this is toincrease the prototype filter order and trade off temporal resolution.The second way, discussed here, is to use an even higher oversamplingratio, which results in more significant filter rolloff at the bandedges.

FIG. 11( b) illustrates the subband structure for Path 1 of the filterbank of FIG. 10 in accordance with the present invention.

Here, pass bands 1132, 1136, 1140, 1144, . . . of the 4× oversampledsubbands SB1*, SB1, SB5, SB9, . . . are provided, with band edges 1130,1134, 1138, . . . The corresponding idealized pass bands 1132′, 1136′,1140′, 1144′, . . . are also shown.

X_(Path-1)(_(ω)) designates the signal in Path 1 (1020), as shown inFIG. 10.

FIG. 11( c) illustrates the subband structure for Path 2 of the filterbank of FIG. 10 in accordance with the present invention.

Here, pass bands 1152, 1156, 1160, . . . of the 4× oversampled subbandsSB2, SB6, SB10, . . . are provided, with band edges 1150, 1154, 1158, .. . The corresponding idealized pass bands 1152′, 1156′, 1160′, . . .are also shown.

X_(Path-2)(_(ω)) designates the signal in Path 2 (1030), as shown inFIG. 10.

FIG. 11( d) illustrates the subband structure for Path 3 of the filterbank of FIG. 10 in accordance with the present invention.

Here, pass bands 1182, 1186, . . . of the 4× oversampled subbands SB2,SB6, SB10, . . . are provided, with band edges 1180, 1184, 1188, . . .The corresponding idealized pass bands 11821′, 11861′, are also shown.

X_(Path-3)(_(ω)) designates the signal in Path 3 (1040), as shown inFIG. 10.

FIG. 12( a) illustrates an original 2-D signal (image) region withseveral subregions for processing in accordance with the presentinvention.

The image 1200 is shown as including a number of subregions A-P.Typically, image data is processed by subdividing it into severalblocks, each of which includes many pixels. A block-based spatialtransform, such as the Discrete Cosine Transform (DCT) is often used, toprovide frequency domain coefficients. Other possible transforms includethe Discrete Fourier Transform, Karhunen-Loeve Transform, Walsh HadamardTransform, and wavelet transform, as well as other known transforms.

FIG. 12( b) provides a graphical depiction of a conventional 2-D,critically-sampled filter bank.

Note that FIGS. 12( b)–13(e) are diagrammatic illustrations that show acomposite of image data in the frequency domain (such as DCT frequencycoefficients or the like) and associated filters.

Each filter in the image/filter composite 1200′ is labeled with (x,y)coordinates, and is overlaid on the corresponding image data subregionwhich it processes. Note that x and y are used to denote horizontal andvertical direction, respectively, and should not be confused with theinput or output signals x(n) and y(n). The meaning should be clear fromthe context.

An 8×8 2-D filter bank is assumed for illustration purposes, althoughdifferent sizes can be used.

For example, an image subregion 1210 has data that is processed by afilter labeled (7,7). The image data within the subregion 1210, which ispart of the larger image subregion “P”, is passed through a pass band1212 of the corresponding filter, while image data beyond the band edges1214 will not be passed by this filter.

However, the 2-D, critically-sampled filter bank suffers from the sameproblem of aliasing between subbands as discussed for the 1-D criticallysampled filter bank.

FIG. 13( a) provides a graphical depiction of a path with no frequencyshift (Path 0) in a 2-D, over-sampled filter bank in accordance with thepresent invention.

As explained further in connection with FIG. 14, a 2× oversampled 2-Dfilter bank structure in accordance with the present invention processesimage or other 2-D data in four processing paths, namely Paths 0–3.

In a particular embodiment, the 2-D data toward the center of each imageregion is processed in the first path, Path 0, while data at verticalboundaries between regions (x-axis shifted by _(π)/M) is processed in asecond path, Path-1, data at horizontal boundaries between regions(y-axis shifted by _(π)/M) is processed in a third path, Path-2, anddata at corners of the boundaries between regions (x-axis and y-axisshifted by _(π)/M) is processed in a fourth path, Path-3.

Here, each filter is labeled with (P,x,y) coordinates in theimage/filter composite 1300-0, where the “P” coordinate denotes thepath, and is shown overlaid with the corresponding image data subregion.For example, an image subregion 1310, labeled “H”, has data that isprocessed by an oversampled filter (0,1,3).

The image data toward the center of the subregion 1310 will pass througha pass band 1312 of the corresponding filter essentially unchanged,while data between the pass band 1312 and band edges 1316 is stopped bya stop band 1314.

FIG. 13( b) provides a graphical depiction of a path with a horizontalfrequency shift (Path 1) in a 2-D, over-sampled filter bank inaccordance with the present invention.

In this path, the image/filter composite 1300-1 shows that data atvertical boundaries between regions (x-axis shifted by _(π)/M) isprocessed using the corresponding filters as shown. For example, databetween the regions “A” and “B” is processed using a filter with index(1,0,1).

FIG. 13( c) provides a graphical depiction of a path with a verticalfrequency shift (Path 2) in a 2-D, over-sampled filter bank inaccordance with the present invention.

In this path, the image/filter composite 1300-2 shows that data athorizontal boundaries between regions (y-axis shifted by _(π)/M) isprocessed using the corresponding filters as shown. For example, databetween the regions “A” and “E” is processed using a filter with index(2,1,0).

FIG. 13( d) provides a graphical depiction of a path with horizontal andvertical frequency shifts (Path 3) in a 2-D, over-sampled filter bank inaccordance with the present invention.

In this path, the image/filter composite 1300-3 shows that data atcorners of the boundaries between regions (x-axis and y-axis shifted by_(π)/M) is processed in a fourth path. For example, data at the cornerof regions “A”, “B”, “E” and “F” is processed using a filter with index(3,1,1).

FIG. 13( e) provides a graphical depiction of the frequency regions thatare processed in FIGS. 13( a)–13(d) in a 2-D, over-sampled filter bankin accordance with the present invention.

The image/filter composite 1300 shows the aggregation of the 2-D dataregions that are processed by each of the four paths. In the exampleshown, sixteen regions are processed in each path, for a total ofsixty-four regions.

A region 1385 illustrates an area of imperfect reconstruction by thefilter banks. Thus, by summing the regions from FIGS. 13( a), (b), (c)and (d), we find that the area 1385 is not covered by any of the fourpaths. To obtain complete coverage, additional processing paths can beintroduced. This is similar to the 1-D case, where we decided to dropthe last subband. Notice that the area 1385 corresponds tohigh-frequency regions of the 2-D signal, so, for most applications,this data is not used at all and can be discarded without noticeablyimpairing the resulting output signal quality.

Generally, the present invention can be extended to an oversampledfilter bank structure for use with N-dimensions. For illustrationpurposes, an example of a 2-D oversampled filter bank has been shown.Such a filter bank can be used, e.g., in applications relating to videoor image processing.

FIG. 14 illustrates a real filter structure for two-dimensional filterbank processing with 2×-oversampled real filter banks in four subbandpaths in accordance with the present invention.

Note that the frequency shift functions described herein can beimplemented as discussed previously (e.g., in connection with FIGS. 4(a), 4(b), 5 and 6) with modification as required for the magnitude anddirection of frequency shift.

Additionally, the filter structure can be modified to used one or morecomplex filters as discussed in connection with FIG. 2( c).

The filter structure 1400 includes processing paths 1410, 1420, 1430 and1440. Generally, a number of delay elements (in path 0: 252-0, 252-0′,252-0″, 252-0′″; in path 1: 252-1, 252-1′; and, in path 2: 252-2,252-2′) are provided to compensate for the processing time of thefunctions that are shown as vertically aligned in the figure.

Each path includes an analysis filter bank 1414-0, 1414-1, 1414-2 and1414-3, and a corresponding synthesis filter bank 1416-0, 1416-1, 1416-2and 1416-3, which receives the corresponding data from the subbandprocessor 240′″.

Path 1 (1420) includes counterpart x-axis frequency shifters 1412-1 and1418-1, while Path 2 (1430) includes counterpart y-axis frequencyshifters 1413-2 and 1417-2, and Path 3 (1440) includes both counterpartx-axis frequency shifters 1412-3 and 1418-3, and counterpart y-axisfrequency shifters 1413-3 and 1417-3.

A combiner 260′ receives the output in each path to provide the finaloutput signal y(n). Again, the x-axis and y-axis terminology should notbe confused with the input signal x(n) and output signal y(n).

Note that the x-axis (1412-1, 1412-3) and y-axis (1413-2, 1413-3) shiftfunctions can use common hardware and/or software.

Accordingly, it can be seen that the present invention provides anoversampled filter bank structure that can be implemented using popularand efficient fast filter banks. Advantageously, aliasing betweensubbands is substantially reduced, thus allowing the independentprocessing of the subband signals using any known subband processingtechnique. For example, an input audio or video signal may be processedto embed auxiliary data in its subbands. The auxiliary data may be usedfor any number of purposes, such as copyright protection, broadcastverification, identification of soundtrack, carrying electronic coupondata, and so forth. Moreover, equalizing and noise shaping of thesubbands as well as other processing may be provided.

Additionally, the oversampled filter bank can be used in OFDM, which hasfound application in Digital Subscriber Loop (DSL) and digital broadcastsystems.

In a particular embodiment, even subbands of an input signal arefrequency-shifted prior to filtering and subband processing, while theodd subbands are delayed to compensate for the processing time of thefrequency shifting. Separate analysis and synthesis filter banks may beprovided for the even and odd subbands, or the subbands may be processedtogether in a single complex filter bank.

2× oversampling may be advantageously used in the filter banks.

Frequency shifting may be achieved using critically-sampled cosinefilter banks, or a Hilbert transform, for example.

In an optional embodiment, the subbands are processed in four subbandpaths, and 4× oversampling is used at the filter banks. The inventionmay also be extended to two-dimensional or higher filteringapplications.

Moreover, the invention can be extended to multi-dimensionalapplications. For example, a 2-D oversampled filter bank structure isshown that processes data in four paths, three of which undergofrequency shifts. The structure is suited for processing image or other2-D data, such as seismic or other vibrational data, temperature dataand the like.

The invention can be extended using the principles shown to additionaldimensions.

Although the invention has been described in connection with variousspecific embodiments, those skilled in the art will appreciate thatnumerous adaptations and modifications may be made thereto withoutdeparting from the spirit and scope of the invention as set forth in theclaims.

For example, known computer hardware, firmware and/or softwaretechniques may be used to implement the invention.

Also, the digital input signal discussed herein may only be a portion ofan overall signal that is provided at some upstream location. Only aportion of the overall signal need be processed in accordance with theinvention. Additionally, the system of the invention may be aggregatedto process additional input signals, or additional portions of an inputsignal.

1. A digital filter apparatus for processing a digital input signal,comprising: oversampled analysis filter bank means for filtering atleast a first and second plurality of subbands of said digital inputsignal according to an oversampling ratio; and a first frequency shifterfor frequency-shifting the first plurality of subbands of said digitalinput signal to provide corresponding frequency-shifted subbands forfiltering by said filter bank means; wherein: said second plurality ofsubbands are distinct from said first plurality of subbands; and theoversampling ratio is selected to reduce aliasing between adjacent onesof the subbands.
 2. The apparatus of claim 1, wherein: the oversamplingratio is 2:1.
 3. The apparatus of claim 1, wherein: said filter bankmeans comprises at least one comb filter.
 4. The apparatus of claim 1,wherein: said filter bank means outputs M subbands, where M≧8.
 5. Theapparatus of claim 1, wherein: said first plurality of subbands compriseeven-numbered subbands of said digital input signal; and said secondplurality of subbands comprise odd-numbered subbands of said digitalinput signal.
 6. The apparatus of claim 1, wherein: said first frequencyshifter comprises critically-sampled cosine-modulated analysis andsynthesis filter banks.
 7. The apparatus of claim 1, wherein: said firstfrequency shifter comprises a Hilbert transformer.
 8. The apparatus ofclaim 1, further comprising: first and second parallel paths forcarrying said digital input signal to said filter bank means; whereinsaid first frequency shifter is provided in said first path; and a firstdelay is provided in said second path for delaying the second pluralityof subbands to compensate for a delay caused by a processing time ofsaid first frequency shifter.
 9. The apparatus of claim 8, wherein: saidfilter bank means comprises a first oversampled analysis filter bankarranged in said first path for filtering said frequency-shiftedsubbands, and a second oversampled analysis filter bank arranged in saidsecond path for filtering the delayed subbands.
 10. The apparatus ofclaim 9, wherein: said first and second analysis filter banks compriserespective M/2-band filter banks, and M is the number of subbands outputfrom the filter bank means.
 11. The apparatus of claim 1, furthercomprising: a subband processor for processing the frequency-shiftedsubbands and the second plurality of subbands after filtering thereof.12. The apparatus of claim 11, further comprising: oversampled synthesisfilter means for filtering said frequency-shifted subbands afterprocessing thereof at said subband processor, and for filtering saidsecond plurality of subbands after processing thereof at said subbandprocessor.
 13. The apparatus of claim 12, further comprising: a secondfrequency shifter for frequency-shifting said frequency-shifted subbandsafter filtering thereof at said synthesis filter means in a shiftdirection opposite to a shift direction of said first frequency shifter.14. The apparatus of claim 13, wherein: said first frequency shifterprovides a frequency upshift, and said second frequency shifter providesa corresponding frequency down shift.
 15. The apparatus of claim 13,further comprising: a second delay for delaying the second plurality ofsubbands to compensate for a delay of said second frequency shifter. 16.The apparatus of claim 12, further comprising: a combiner for combiningsaid frequency-shifted subbands after filtering thereof at saidsynthesis filter means, with said second plurality of subbands afterfiltering thereof at said synthesis filter means, to provide a digitaloutput signal corresponding to said digital input signal.
 17. Theapparatus of claim 12, wherein: said synthesis filter means comprises afirst oversampled synthesis filter bank for synthesis filtering saidfrequency-shifted subbands, and a second oversampled synthesis filterbank for synthesis filtering said second plurality of subbands.
 18. Theapparatus of claim 17, wherein: said first and second oversampledsynthesis filter banks comprise respective comb filters.
 19. Theapparatus of claim 1, wherein: said first frequency shifter provides aπ/M radian frequency shift; and M is the number of subbands output fromsaid filter bank means.
 20. The apparatus of claim 1, wherein said firstfrequency shifter comprises: a cosine-modulated analysis filter bank forprocessing the first plurality of subbands; means for providingfrequency axis reversal for the subbands output from thecosine-modulated analysis filter bank; and a cosine-modulated synthesisfilter bank for processing the subbands output from the frequency axisreversal means to provide the frequency-shifted subbands.
 21. Theapparatus of claim 1, wherein said first frequency shifter comprises: acosine-modulated analysis filter bank for processing the first pluralityof subbands; a cosine-modulated synthesis filter bank for processing thesubbands output from the cosine-modulated analysis filter bank toprovide the frequency-shifted subbands; and means for feeding a highestsubband that is output from the cosine-modulated analysis filter bank toa lowest subband input of the cosine-modulated synthesis filter bank.22. The apparatus of claim 1, wherein said filter bank means comprises acomplex filter bank, further comprising: a delay for delaying the secondplurality of subbands to compensate for a delay of said first frequencyshifter; and means for forming a complex signal comprising a realportion obtained from the frequency-shifted subbands, and an imaginaryportion obtained from the delayed subbands; and means for providing thecomplex signal to the complex filter bank for filtering thereat.
 23. Theapparatus of claim 1, wherein: said oversampled analysis filter bankmeans is adapted to filter additional subbands of said digital inputsignal, including at least a third and fourth plurality of subbands ofsaid digital input signal according to the oversampling ratio; wherein:said third plurality of subbands are distinct from said fourth pluralityof subbands.
 24. The apparatus of claim 23, wherein: said oversamplingratio is 4:1.
 25. The apparatus of claim 23, further comprising: first,second, third and fourth parallel paths for providing said digital inputsignal to said analysis filter bank means; the first frequency shifterbeing provided in said first path for frequency-shifting said firstplurality of subbands; a second frequency shifter in said second pathfor frequency-shifting said second plurality of subbands; a thirdfrequency shifter in said fourth path for frequency-shifting said thirdplurality of subbands; and a delay in said third path for delaying saidfourth plurality of subbands to compensate for a processing time of saidfirst, second and third frequency-shifters.
 26. The apparatus of claim25, wherein: said first frequency shifter provides a π/M radianfrequency shift; said second frequency shifter provides a π/2M radianfrequency shift; said third frequency shifter provides a −π/2M radianfrequency shift; and 2M is the number of subbands output from theoversampled analysis filter bank means.
 27. The apparatus of claim 25,wherein: said analysis filter bank means comprises M/2-band oversampledfilter banks for each of said first, second, third and fourth paths, and2M is the number of subbands output from the oversampled analysis filterbank means.
 28. The apparatus of claim 27, wherein: said M/2-bandoversampled filter banks comprise comb filters.
 29. A digital filterapparatus for processing a digital input signal, comprising: oversampledanalysis filter bank means for filtering at least a first and secondplurality of subbands of said digital input signal according to anoversampling ratio; said second plurality of subbands are distinct fromsaid first plurality of subbands; the oversampling ratio is selected toreduce aliasing between adjacent ones of the subbands; said oversampledanalysis filter bank means is adapted to filter additional subbands ofsaid digital input signal, including at least a third and fourthplurality of subbands of said digital input signal according to theoversampling ratio; said third plurality of subbands are distinct fromsaid fourth plurality of subbands; wherein the digital input signalcomprises two-dimensional data extending along an x-axis and aperpendicular y-axis, further comprising: first, second, third andfourth parallel paths for providing said digital input signal to saidanalysis filter bank means; x-axis frequency shifting means forfrequency-shifting said second plurality of subbands in said secondpath, and said fourth plurality of subbands in said fourth path; y-axisfrequency shifting means for frequency-shifting said third plurality ofsubbands in said third path, and said fourth plurality of subbands insaid fourth path; and delay means for delaying said first plurality ofsubbands in said first path to compensate for a processing time of saidx-axis and y-axis frequency shifting means.
 30. The apparatus of claim29, wherein: said x-axis and y-axis frequency shifting means provide amagnitude _(π)/M radian frequency shift; and 4×M×M is the number ofsubbands output from the oversampled analysis filter bank means.
 31. Theapparatus of claim 29, wherein: said analysis filter bank meanscomprises M/2-band oversampled filter banks for each of said first,second, third and fourth paths, and 4×M×M is the number of subbandsoutput from the oversampled analysis filter bank means.
 32. Theapparatus of claim 31, wherein: said M/2-band oversampled filter bankscomprise comb filters.